Formal Verification Checked a 10,000-Page Proof, Found a Gap, Produced a New Theorem

Some modern proofs run to ten thousand pages, too long for anyone to read fully, so formal verification translates each step into machine-checkable statements. In one run the tool found an incomplete citation mid-chapter: one step's conclusion did not imply the next without an extra condition, a gap human reviewers missed for years. The side effect matters most: after the condition was added, the run produced a corollary nobody had recorded, later organized into a new theorem. Formal tools do not just inspect proofs, they can participate in discovery.